中国科学院数学与系统科学研究院期刊网

15 November 2019, Volume 35 Issue 11
    

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  • Anuradha GUPTA, Bhawna GUPTA
    Acta Mathematica Sinica. 2019, 35(11): 1729-1740. https://doi.org/10.1007/s10114-019-8331-7
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    In this paper, we generalize the concept of asymptotic Hankel operators on H2(D) to the Hardy space H2(Dn) (over polydisk) in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence. Meanwhile, we introduce ith-partial Hankel operators on H2(Dn) and obtain a characterization of its compactness for n > 1. Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn). It is also shown that a Toeplitz operator with symbol φ is asymptotic Hankel if and only if φ is holomorphic function in L(Tn).
  • Hai Xia YU, Jun Feng LI
    Acta Mathematica Sinica. 2019, 35(11): 1741-1759. https://doi.org/10.1007/s10114-019-8270-3
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    In this paper, the weak (1, 1) boundedness of oscillatory singular integral with variable phase P (x)γ(y) for any x, y ∈ R,
    Tf(x):=p. v.∫-∞ eiP(x)γ(y)f(x-y) dy/y
    is studied, where P is a real monic polynomial on R.
  • Xu ZHANG, Xin Xing WU
    Acta Mathematica Sinica. 2019, 35(11): 1760-1770. https://doi.org/10.1007/s10114-019-8510-6
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    This paper studies the M0-shadowing property for the dynamics of diffeomorphisms defined on closed manifolds. The C1 interior of the set of all two dimensional diffeomorphisms with the M0-shadowing property is described by the set of all Anosov diffeomorphisms. The C1-stably M0-shadowing property on a non-trivial transitive set implies the diffeomorphism has a dominated splitting.
  • Li ZHANG, Wan Tong LI, Zhi Cheng WANG, Yu Juan SUN
    Acta Mathematica Sinica. 2019, 35(11): 1771-1794. https://doi.org/10.1007/s10114-019-8294-8
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    This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves. We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds.
  • Liang TIAN, Wei GUO, Kui JI
    Acta Mathematica Sinica. 2019, 35(11): 1795-1806. https://doi.org/10.1007/s10114-019-8509-z
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    In this note, we study a rich operator class denoted by PBn(Ω) which includes all homogeneous operators and quasi-homogeneous operators in the Cowen-Douglas class. A complete unitarily classification theorem is given. Furthermore, we also concern the curvature and similarity of operators in PBn(Ω).
  • Qing MENG, Li Guang WANG
    Acta Mathematica Sinica. 2019, 35(11): 1807-1816. https://doi.org/10.1007/s10114-019-9024-y
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    We study property T for an action α of a discrete group Γ on a unital C*-algebra A. Our main results improve some well-known results about property T for groups. Moreover, we introduce Hilbert A -module property T and show that the action α has property T if and only if the reduced crossed product A×α,r Γ has Hilbert A -module property T.
  • Tao WANG, Ming Ju LIU, De Ming LI
    Acta Mathematica Sinica. 2019, 35(11): 1817-1826. https://doi.org/10.1007/s10114-019-8500-8
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    Let G be a graph with vertex set V (G), edge set E(G) and maximum degree Δ respectively. G is called degree-magic if it admits a labelling of the edges by integers {1, 2, …,|E(G)|} such that for any vertex v the sum of the labels of the edges incident with v is equal to (1+|E(G)|)/2·d(v), where d(v) is the degree of v. Let f be a proper edge coloring of G such that for each vertex vV (G),|{e:eEv, f(e) ≤ Δ/2}|=|{e:eEv, f(e) > Δ/2}|, and such an f is called a balanced edge coloring of G. In this paper, we show that if G is a supermagic even graph with a balanced edge coloring and m ≥ 1, then (2m + 1)G is a supermagic graph. If G is a d-magic even graph with a balanced edge coloring and n ≥ 2, then nG is a d-magic graph. Results in this paper generalise some known results.
  • Xun Xiang GUO
    Acta Mathematica Sinica. 2019, 35(11): 1827-1840. https://doi.org/10.1007/s10114-019-8527-x
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    In this paper, we give an operator parameterization for the set of dilations of a given pair of dual g-frames and the set of dilations of pairs of dual g-frames of a given g-frame. In particular, for the dilations of a given pair of dual g-frames, we introduce the concept of joint complementary g-frames and prove that the joint complementary g-frames of a pair of dual g-frames are unique in the sense of joint similarity, which then helps to obtain a sufficient condition such that the complementary g-frames of a g-frame are unique in the sense of similarity and show that the set of dilations of a given dual g-frame pair are parameterized by a set of invertible diagonal operators. For the dilations of pairs of dual g-frames, we prove that the set of dilations of pairs of dual g-frames are parameterized by a set of invertible upper triangular operators.
  • Jiao CHEN, Liang HUANG
    Acta Mathematica Sinica. 2019, 35(11): 1841-1853. https://doi.org/10.1007/s10114-019-8071-8
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    The main purpose of this paper is to establish, using the Littlewood-Paley-Stein theory (in particular, the Littlewood-Paley-Stein square functions), a Calderón-Torchinsky type theorem for the following Fourier multipliers on anisotropic Hardy spaces Hp(Rn; A) associated with expensive dilation A:
    ???20191109
    Our main Theorem is the following:Assume that m(ξ) is a function on Rn satisfying
    ???20191109-1
    with s > ζ--1(1/p-1/2). Then Tm is bounded from Hp(Rn; A) to Hp(Rn; A) for all 0 < p ≤ 1 and
    ???20191109-2
    where A* denotes the transpose of A. Here we have used the notations mj(ξ)=m(A*jξ)φ(ξ) and φ(ξ) is a suitable cut-off function on Rn, and Ws(A*) is an anisotropic Sobolev space associated with expansive dilation A* on Rn.
  • Zhan Qiang BAI, Wei XIAO
    Acta Mathematica Sinica. 2019, 35(11): 1854-1860. https://doi.org/10.1007/s10114-019-9069-y
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    The Gelfand-Kirillov dimension is an invariant which can measure the size of infinitedimensional algebraic structures. In this article, we show that it can also measure the reducibility of scalar generalized Verma modules. In particular, we use it to determine the reducibility of scalar generalized Verma modules associated with maximal parabolic subalgebras in the Hermitian symmetric case.